Synapse

Synapse is the "New Continent" that Sugata was researching the whole time and found out that this is connected to Tomoki's dream. The only way for them to enter Synapse is the Dive Game. In his findings, he finds that some people on earth are not "real", but in fact are just angels dreaming. The "Man of Synapse" sent Nymph from here to bring Ikaros back. The plan was a failure, and Nymph eventually joined Tomoki. He also sent Astrea to kill Tomoki, however, that plan was a failure as well, and Astrea broke the chain on her choaker, meaning that she left the Man of Synapse. Later in the anime, the Man of Synapse created the 2nd Generation Angeloids, an even more powerful version of the first generation angeloids. The first of these brand-new 2nd Generation Angeloids we saw was Chaos, an Angeloid who did not have wings, but a floating device that appeared as three large purple blades behind her. The Man of Synapse has also sent her to kill Tomoki.

The Synapse first appears a grassy field, thru Tomoki's dreams. However, later when Sugata keeps re-entering it, we find out it is just sky with little pieces of "islands" floating there. Some islands are organic, others are not.

Tomoki, Sohara, Sugata, and Mikako visited an island with a single large structure that had writings on it (as seen on the picture). It is rumored that these are the rules that Angeloids must follow, however, there aren't enough details to confirm it.